Desenvolvimento do raciocínio proporcional: uma sequência didática para o sexto ano do ensino fundamental

Abstract

This work, carried out during the Masters Course for teaching Science and Mathematics, within the postgraduate program in teaching Science and Mathematics at the Pontal College of Integrated Sciences of the Federal University of Uberlândia. It a aims to introduce a didactic sequence to encourage the development of proportional reasoning with the theoretical support the Theory of Conceptual Fields (TCC) by Gerard Vergnaud. The specific objectives are: (a) to analyze a didactic sequence, arranged in the form of problem situations in order to promote the establishment of relations of covariance and invariance of quantities, required to conceptualize reason and proportion and (b) examine the performance and the strategies used by the students to solve problem situations involving proportional reasoning, through the application of didactic proposal. The work has methodological support in Teaching Engineering and was developed together with approximately 26 students of the sixth grade of an elementary school in the city of Ituiutaba, Minas Gerais, during regular class periods. The sequence had six stages, the first was a pencil and paper type evaluation and review the following stages were composed of problem situations applied with mediation of a teacher as well as evaluations, being that these instruments have been drawn up on the basis of the existing literature on the subject of proportional reasoning. Data was analyzed through quantitative and qualitative descriptive statistics when the categories of analysis were set up. In the first step, there was more difficulty with the problems of comparison than those of omissive value and the multiplicative strategies used by the students indicated some inference and prediction on the understanding that the values involved in the problems varied together. Throughout the implementation of the result, it was found that the students have come to identify the proportional quantities involved in situations and most of them managed to justify the answers through the relationship of covariance, using the appropriate symbol. The methodological option of offering diverse situations before the formal presentation of this content (which happens from the seventh grade of primary school) helps to develop proportional reasoning of students. It is expected that the analysis and theoretical discussions undertaken in this work could contribute to the work of a Maths teacher.